How does mean and standard deviation values affect the performance in maximum likelihood estimate? Is the that the higher the mean and the standard values, the better the maximum likelihood estimation or the lower the mean and the standard values, the better the maximum likelihood estimation? what is the right interpretation?
Based on Central Theorme Limit assumptions, the original effect is the size of the sample, so, if such, (for n large) : we have the ML estimates properties:
- they become unbiased minimum variance estimators as the sample size increases
- they have approximate normal distributions and approximate sample variances that can be calculated and used to generate confidence bounds
- likelihood functions can be used to test hypotheses about models and parameters
- so, the mean estimation of any parameter ,E(theta), affect the performance of ML estimation via the "bias" , and they will affect the CIs calculations.
Based on the sample size, large standard deviation values obtained from data with defined mean can reduce the performance in a maximum likelihood performance as this suggests low dynamic range
Under a normal population assumption the sample mean and variance are both maximum likelihood estimators of the corresponding population parameters.. For full details see the attached file. As you will notice your question thus doesn't make sense. I suggest you look at the attached file and then ask a variation of the original question. Best wishes, David Booth
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